A new variational calculation for N-dimensional polarons in the strong-coupling limit

Area of Science:

• Condensed matter physics
• Quantum mechanics

Background:

• Polarons, quasiparticles formed by electron-phonon interactions, are crucial in materials science.
• Calculating polaron ground-state energy, especially in the strong-coupling limit, is computationally challenging.
• Existing methods like Feynman path integrals have limitations in accuracy and applicability.

Purpose of the Study:

• To develop a novel variational approach for calculating polaron ground-state energy.
• To apply this method in arbitrary N dimensions, focusing on the strong-coupling regime.
• To validate the approach by comparing results with established literature values.

Main Methods:

• Utilizing a phonon coherent state to represent the phonon wavefunction.
• Deriving a self-consistent integro-differential equation for the electron wavefunction.
• Applying the method for N=1, 2, and 3 dimensions.

Main Results:

• The approach yields accurate ground-state energy calculations for polarons in N=1, 2, and 3 dimensions.
• Results show good agreement with the best available literature values.
• For arbitrary N dimensions, the method's results are slightly lower (by small percentages) than those from Feynman path integrals.

Conclusions:

• The novel variational approach provides a reliable and accurate method for polaron ground-state energy calculation.
• The method demonstrates high precision, especially in the strong-coupling regime.
• The proposed approach is suggested to be universally applicable to polaron systems under strong coupling conditions.